E8 Quiver Gauge Theory and Mirror Symmetry

TL;DR

This paper establishes a mirror symmetry between E8 quiver gauge theories and strongly coupled superconformal theories, linking their Higgs and Coulomb branches and suggesting a broader duality framework.

Contribution

It demonstrates a Higgs-Coulomb branch identity for E8 quiver theories and proposes a mirror symmetry with strongly coupled gauge theories.

Findings

Higgs branch of E8 quiver matches Coulomb branch of E8 superconformal theory

Extends Higgs-Coulomb identity to all ADE types

Provides interpretation of parameters via Hanany-Witten setup

Abstract

We show that the Higgs branch of a four-dimensional Yang-Mills theory, with gauge and matter content summarised by an E_8 quiver diagram, is identical to the generalised Coulomb branch of a four-dimensional superconformal strongly coupled gauge theory with E_8 global symmetry. This is the final step in showing that there is a Higgs-Coulomb identity of this kind for each of the cases {0}, A_1, A_2, D_4, E_6, E_7 and E_8. This series of equivalences suggests the existence of a mirror symmetry between the quiver theories and the strongly coupled theories. We also discuss how to interpret the parameters of the quiver gauge theory in terms of the Hanany-Witten picture.